SOLUTION: Find the point of intersection of the planes x + y + z = 12, 2x + y - z = 20, and -x - y + 4z = - 17

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Question 1091455: Find the point of intersection of the planes x + y + z = 12, 2x + y - z = 20, and -x - y + 4z = - 17
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x + y + z = 12
2x + y - z = 20
-x - y + 4z = - 17
x + y + z = 12
------------------------- Add eqn 1 & 3
5z = -5
z = -1
---------
x + y + z = 12
2x + y - z = 20
================
x + y = 13
2x + y = 19
---------------
Subtract
-x = -6
x = 6
----------------
x + y + z = 12
6 + y - 1 = 12
y = 7
--> intersection at (6,7,-1)